The individual modules in the special-functions sub-collection can also be made available as describes in the sections below.

5.1Error Functions

The error function is described in Abramowitz and Stegun [Abramowitz64], Chapter 7. The functions are defined in the "error.ss" file in the special-functions sub-collection of the science collection and are made available using the form:

5.2Exponential Integral Functions

Information on the exponential integral functions can be found in Abramowitz and Stegun [Abramowitz64], Chapter 5. The functions are defined in the "exponential-integral.ss" file in the special-functions sub-collection of the science collection are made available using the form:

Note that the gamma functions (Section 5.3), psi functions (Section 5.4), and the zeta functions (Section 5.5) are defined in the same module, "gamma.ss". This is because their definitions are interdependent and PLT Scheme does not allow circular module dependencies.

Computes the gamma function, Γ(x), subject to x not being a negative integer. This function is computed using the real Lanczos method. The maximum value of x such that Γ(x) is not considered an overflow is given by the constant gamma-xmax and is 171.0.

Computes the logarithm of the gamma function, log Γ(x), subject to x not being a negative integer. For x < 0, the real part of log Γ(x) is returned, which is equivalent to log |Γ(x)|. The function is computed using the real Lanczos method.

Computes the logarithm of the magnitude of the gamma function and its sign, subject to x not being a negative integer, and returns them as multiple values. The function is computed using the real Lanczos method. The value of the gamma function can be reconstructed using the relation Γ(x) = sgn × exp(resultlg), where resultlg and sgn are the returned values.

Note that the gamma functions (Section 5.3), psi functions (Section 5.4), and the zeta functions (Section 5.5) are defined in the same module, "gamma.ss". This is because their definitions are interdependent and PLT Scheme does not allow circular module dependencies.

5.5Zeta Functions

The Riemann zeta function is defined in Abramowitz and Stegun [Abramowitz64], Section 23.3. The zeta functions are defined in the "gamma.ss" file in the special-functions subcollection of the science collection are are made available using the form:

Note that the gamma functions (Section 5.3), psi functions (Section 5.4), and the zeta functions (Section 5.5) are defined in the same module, "gamma.ss". This is because their definitions are interdependent and PLT Scheme does not allow circular module dependencies.